Dynamics Of Complex Molecular Systems Research Articles

Electronically Nonadiabatic Dynamics in Complex Molecular Systems: An Efficient and Accurate Semiclassical Solution

Chemical reaction dynamics is always a central theme in chemistry research. In many important chemical processes, reaction dynamics is electronically nonadiabatic, i.e., dynamics involves coupled multiple electronic states. We demonstrate in this paper that a semiclassical (SC) treatment based on an initial value representation methodology and a classical mapping formalism for the electronic degrees of freedom is now able to provide a rigorous and practical solution to electronically nonadiabatic dynamics in complex molecular systems. The key component of this treatment is to incorporate a correlated importance sampling protocol in nonadiabatic SC calculations, which results in a speedup factor of 100 or more in comparison with that using the standard sampling approach. This is illustrated by application to a two-state model coupled with up to 10 nuclear bath modes for a benchmark nonadiabatic excitation energy transfer problem. This work provides great opportunities for the effectively theoretical investigations on reaction mechanisms in complex molecular systems, in which electronically nonadiabatic dynamics plays an importance role.

ChemInform Abstract: Linear‐Scaling Quantum Mechanical Methods for Excited States

AbstractReview: 70 refs.

The history of X-ray free-electron lasers

The successful lasing at the SLAC National Accelerator Laboratory of the Linear Coherent Light Source (LCLS), the first X-ray free-electron laser (X-ray FEL), in the wavelength range 1.5 to 15 Å, pulse duration of 60 to few femtoseconds, number of coherent photons per pulse from 1013 to 1011, is a landmark event in the development of coherent electromagnetic radiation sources. Until now electrons traversing an undulator magnet in a synchrotron radiation storage ring provided the best X-ray sources. The LCLS has set a new standard, with a peak X-ray brightness higher by ten orders of magnitudes and pulse duration shorter by three orders of magnitudes. LCLS opens a new window in the exploration of matter at the atomic and molecular scales of length and time. Taking a motion picture of chemical processes in a few femtoseconds or less, unraveling the structure and dynamics of complex molecular systems, like proteins, are some of the exciting experiments made possible by LCLS and the other X-ray FELs now being built in Europe and Asia. In this paper, we describe the history of the many theoretical, experimental and technological discoveries and innovations, starting from the 1960s and 1970s, leading to the development of LCLS.

Linear-scaling quantum mechanical methods for excited states

The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems.

Non-adiabatic dynamics of interfacial systems: a case study of a nanoparticle penetration into a lipid bilayer

Understanding the dynamics of complex molecular systems is often facilitated by analysis of underlying free energy landscapes. In particular, activated transitions between metastable states of a system are frequently investigated assuming that the system follows a minimum energy path (MEP) connecting these states. However, the MEP assumption becomes invalid if the timescale of the system relaxation towards the MEP is comparable with the timescale of the system motion along the MEP. We demonstrate that such non-adiabatic dynamics takes place during molecular transport across flexible membranes and interfaces. This phenomenon is illustrated by a case study of penetration of a hydrophobic nanoparticle into a lipid bilayer. This system is investigated using constrained molecular dynamics simulations. Motion of this system along the MEP involves significant changes in the membrane shape in response to the nanoparticle position. It is shown that the timescale associated with these shape changes exceeds the timescale of the translational motion of the nanoparticle, which leads to non-adiabatic coupling between the nanoparticle transport and the membrane fluctuations. Implication of this coupling to analysis of the constrained simulations is discussed.

Experimental evidence for a frustrated energy landscape in a three-helix-bundle protein family

Energy landscape theory is a powerful tool for understanding the structure and dynamics of complex molecular systems, in particular biological macromolecules1. The primary sequence of a protein defines its free energy landscape, and thus determines the folding pathway and the rate constants of folding and unfolding, as well as its native structure. Theory has shown that roughness in the energy landscape will lead to slower folding1, but derivation of detailed experimental descriptions of this landscape is challenging. Simple folding models2,3 show that folding is significantly influenced by chain entropy; proteins where the contacts are local fold fast, due to the low entropy cost of forming stabilising, native contacts during folding4,5. For some protein families, stability is also a determinant of folding rate constants6. Where these simple metrics fail to predict folding behaviour it is probable that there are features in the energy landscape that are unusual. Such general observations cannot explain the folding behaviour of the R15, R16 and R17 domains of α-spectrin. R15 folds ~3000 times faster than its homologues, although they have similar structures, stabilities and, as far as can be determined, transition state stabilities7-10. Here we show that landscape roughness (internal friction) is responsible for the slower folding and unfolding of R16 and R17. We use chimeric domains to demonstrate that this internal friction is a property of the core, and suggest that frustration in the landscape of the slow folding spectrin domains may be due to mis-docking of the long helices during folding. Although theoretical studies have suggested that rugged landscapes will result in slower folding, this is the first time that such a phenomenon has been shown experimentally to directly influence the folding kinetics of a “normal” protein with a significant energy barrier – one which folds on a relatively slow ms-s timescale.

Two-Dimensional Electronic Spectroscopy of Molecular Aggregates

The properties of molecular aggregates, coupled clusters of small molecules, are often challenging to unravel because of their inherent complexity and disordered environments. Their structure-function relationships are often far from obvious. However, their ability to efficiently channel excitation energy over remarkable distances, as is the case in photosynthetic light harvesting, is a compelling motivation to investigate them. Understanding and subsequently mimicking the processes in photosynthesis, for example, will set the stage for considerable advances in using light harvesting to fuel renewable energy technologies. Two-dimensional (2D) electronic spectroscopy is emerging as a nonlinear optical technique that provides significant insight into the interactions and dynamics of complex molecular systems. In addition to spectrally resolving excitation and emission energies over significant bandwidths with femtosecond resolution, this technique has already enabled discoveries about the structure and dynamics of photosynthetic light-harvesting complexes and other aggregates. Multiple capabilities unique to 2D electronic spectroscopy enable such findings. For example, the spectral resolution of excitation and emission combined with the ability to eliminate the effects of static disorder can reveal the homogeneous line width of a transition and the different dynamic contributions to it. Two dimensional spectroscopy is also sensitive to electronic coherence and has been employed to identify and characterize coherent excitation energy transfer dynamics in photosynthetic systems and conjugated polymers. The presence of cross-peaks, signals for which excitation and emission occur at different wavelengths, provides multiple forms of information. First, it allows the identification of states in congested spectra and reveals correlations between them. Second, we can track excitation energy flow from origin to terminus through multiple channels simultaneously. Finally, 2D electronic spectroscopy is uniquely sensitive to intermolecular electronic coupling through the sign and amplitude of the cross-peaks. This feature makes it possible to reveal spatial molecular configurations by probing electronic transitions. Another means of "resolving" these angstrom-scale arrangements is to manipulate the probing laser pulse polarizations. In this way, we can isolate and modulate specific processes in order to retrieve structural information. In this Account, we demonstrate these capabilities through a close collaboration between experiments and modeling on isolated photosynthetic pigment-protein complexes and also on J-aggregates. Each of the probed systems we describe offers insights that have both increased the utility of 2D electronic spectroscopy and led to discoveries about the molecular aggregates' dynamics and underlying structure.

On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.

Laser-field-induced surface-hopping method for the simulation and control of ultrafast photodynamics

We present the semiclassical laser-field-induced surface-hopping method for the simulation and control of coupled electron-nuclear dynamics in complex molecular systems including all degrees of freedom. Our approach is based on the Wigner representation of quantum mechanics. The combination of the molecular dynamics ``on the fly'' employing quantum initial conditions with the surface-hopping procedure allows for the treatment of the electronic transitions induced by the laser field. Our semiclassical approach reproduced accurately exact quantum dynamics in a two-electronic-state model system. We demonstrate the scope of our method on the example of the optimal pump-dump control of the trans-cis isomerization of a prototypical Schiff base molecular switch. Our results show that selective photochemistry can be achieved by shaped laser pulses which open new dynamical pathways by suppressing the isomerization through the conical intersections between electronic states.

Probing dynamics of complex molecular systems with ultrafast 2D IR vibrational echo spectroscopy

Ultrafast 2D IR vibrational echo spectroscopy is described and a number of experimental examples are given. Details of the experimental method including the pulse sequence, heterodyne detection, and determination of the absorptive component of the 2D spectrum are outlined. As an initial example, the 2D spectrum of the stretching mode of CO bound to the protein myoglobin (MbCO) is presented. The time dependence of the 2D spectrum of MbCO, which is caused by protein structural evolution, is presented and its relationship to the frequency-frequency correlation function is described and used to make protein structural assignments based on comparisons to molecular dynamics simulations. The 2D vibrational echo experiments on the protein horseradish peroxidase are presented. The time dependence of the 2D spectra of the enzyme in the free form and with a substrate bound at the active site are compared and used to examine the influence of substrate binding on the protein's structural dynamics. The application of 2D vibrational echo spectroscopy to the study of chemical exchange under thermal equilibrium conditions is described. 2D vibrational echo chemical exchange spectroscopy is applied to the study of formation and dissociation of organic solute-solvent complexes and to the isomerization around a carbon-carbon single bond of an ethane derivative.

Two-dimensional electronic spectroscopy of the B800–B820 light-harvesting complex

Emerging nonlinear optical spectroscopies enable deeper insight into the intricate world of interactions and dynamics of complex molecular systems. 2D electronic spectroscopy appears to be especially well suited for studying multichromophoric complexes such as light-harvesting complexes of photosynthetic organisms as it allows direct observation of couplings between the pigments and charts dynamics of energy flow on a 2D frequency map. Here, we demonstrate that a single 2D experiment combined with self-consistent theoretical modeling can determine spectroscopic parameters dictating excitation energy dynamics in the bacterial B800-B820 light-harvesting complex, which contains 27 bacteriochlorophyll molecules. Ultrafast sub-50-fs dynamics dominated by coherent intraband processes and population transfer dynamics on a picosecond time scale were measured and modeled with one consistent set of parameters. Theoretical 2D spectra were calculated by using a Frenkel exciton model and modified Förster/Redfield theory for the calculation of dynamics. They match the main features of experimental spectra at all population times well, implying that the energy level structure and transition dipole strengths are modeled correctly in addition to the energy transfer dynamics of the system.

Dynamics of complex molecular systems with numerical kinetic energy operators in generalized coordinates

Dynamics of complex molecular systems in generalized coordinates ( q, p) using numerical kinetic energy operators is investigated. The kinematical tools necessary for quantum, classical or semiclassical dynamics with or without constraints mainly come from the covariant and contravariant components of the metric tensor and their derivatives up to the second ones. These quantities are computed numerically but without any other approximation than the numerical precision by the code TNUM. This code generates kinetic energy operators in the internal coordinates of the Z-matrix describing the molecular frame geometry in the ab initio quantum chemistry step or in symmetry adapted coordinates [D. Lauvergnat, A. Nauts, J. Chem. Phys. 116 (2002) 8560]. Various reduced dimensionality models can be used in the upgraded code. The interface with an ab initio code is calibrated on a 22-atom system for which a two-dimensional quantum treatment with a constrained Hamiltonian has been carried out previously. The test application concerns the spreading properties of a wave packet in an unstable flat region around a valley ridge inflexion point between two transition states in the Endo-dimerization of cyclopentadiene. We perform here on-the-fly classical or semiclassical dynamics in full or reduced dimensionality.

Quantum dynamics of complex molecular systems

This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.

Quantum control of energy flow in light harvesting.

Coherent light sources have been widely used in control schemes that exploit quantum interference effects to direct the outcome of photochemical processes. The adaptive shaping of laser pulses is a particularly powerful tool in this context: experimental output as feedback in an iterative learning loop refines the applied laser field to render it best suited to constraints set by the experimenter. This approach has been experimentally implemented to control a variety of processes, but the extent to which coherent excitation can also be used to direct the dynamics of complex molecular systems in a condensed-phase environment remains unclear. Here we report feedback-optimized coherent control over the energy-flow pathways in the light-harvesting antenna complex LH2 from Rhodopseudomonas acidophila, a photosynthetic purple bacterium. We show that phases imprinted by the light field mediate the branching ratio of energy transfer between intra- and intermolecular channels in the complex's donor acceptor system. This result illustrates that molecular complexity need not prevent coherent control, which can thus be extended to probe and affect biological functions.

The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations

The semiclassical (SC) initial value representation (IVR) provides a potentially practical way for adding quantum mechanical effects to classical molecular dynamics (MD) simulations of the dynamics of complex molecular systems (i.e., those with many degrees of freedom). It does this by replacing the nonlinear boundary value problem of semiclassical theory by an average over the initial conditions of classical trajectories. This paper reviews the background and rebirth of interest in such approaches and surveys a variety of their recent applications. Special focus is on the ability to treat the dynamics of complex systems, and in this regard, the forward−backward (FB) version of the approach is especially promising. Several examples of the FB-IVR applied to model problems of many degrees of freedom show it to be capable of describing quantum effects quite well and also how these effects are quenched when some of the degrees of freedom are averaged over (“decoherence”).

Direct imaging of transient molecular structures with ultrafast diffraction.

Ultrafast electron diffraction (UED) has been developed to study transient structures in complex chemical reactions initiated with femtosecond laser pulses. This direct imaging of reactions was achieved using our third-generation apparatus equipped with an electron pulse (1.07 +/- 0.27 picoseconds) source, a charge-coupled device camera, and a mass spectrometer. Two prototypical gas-phase reactions were studied: the nonconcerted elimination reaction of a haloethane, wherein the structure of the intermediate was determined, and the ring opening of a cyclic hydrocarbon containing no heavy atoms. These results demonstrate the vastly improved sensitivity, resolution, and versatility of UED for studying ultrafast structural dynamics in complex molecular systems.

Dynamics of complex molecular systems: Molecular dynamics simulations of enzyme catalysis, polymer growth and phase separations

Abstract Molecular Dynamics (MD) simulations of chemical reactions in condensed fluids are performed by solving the classical mechanical equations of motion in connection with simple transition state activated chemical reactions. This model differs from stochastic models for particle reactions by that MD includes hydrodynamic modes which enter into diffusion limited chemical reactions and domain growth at phase separations. Oscillating chemical reactions, spinodal decomposition under shear flow, polymer growth and diffusion limited enzyme catalysis are all examples where the dynamics are influenced by the hydrodynamics of the condensed fluid.

Mixed semiclassical–classical approaches to the dynamics of complex molecular systems

Starting with the semiclassical initial value representation (IVR) for the description of a composite molecular system consisting of a “system’’ and a “bath,’’ we show a systematic procedure whereby one can retain the semiclassical IVR description of the “system’’—thus including quantum interference and tunneling effects for these degrees of freedom—while neglecting these effects in the “bath’’ degrees of freedom, thus reducing them to a classical description. The zeroth order version of this mixed semiclassical–classical model is seen to be the semiclassical equivalent of the Ehrenfest model (closely related to the TDSCF approximation), but higher order versions are also developed that go beyond this level of approximation. Two levels of this theory are explicitly worked out. Numerical tests on simple but illustrative problems are used to discuss the merit of these approaches.